Area spectral rigidity for axially symmetric symplectic billiard tables
Abstract
We prove that any finitely smooth, axially symmetric, strictly convex domain with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this class is necessarily equi-affine. We use techniques, adapted to symplectic billiards, inspired by the paper of J. De Simoi, V. Kaloshin and Q. Wei [5].
Fields of Study & Subjects
Holomorphic and Operator Theory
Algebraic and Geometric Analysis
Analytic and geometric function theory
Publication details
- Journal / source
- Journal of Modern Dynamics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 22
- Issue
- 0
- Pages
- 469–488
- Publication date
- 1 January 2026
- Language
- EN